Domínguez Vázquez, MiguelGonzález-Álvaro, DavidMouillé, Lawrence2024-10-042024-10-042023Domínguez-Vázquez, M., González-Álvaro, D. & Mouillé, L. Infinite families of manifolds of positive kth-intermediate Ricci curvature with k small. Math. Ann. 386, 1979–2014 (2023). https://doi.org/10.1007/s00208-022-02420-whttp://hdl.handle.net/10347/35009Positive kth-intermediate Ricci curvature on a Riemannian n-manifold, to be denoted by Ric_k > 0, is a condition that interpolates between positive sectional and positive Ricci curvature (when k = 1 and k = n − 1 respectively). In this work, we produce many examples of manifolds of Ric_k > 0 with k small by examining symmetric and normal homogeneous spaces, along with certain metric deformations of fat homogeneous bundles. As a consequence, we show that every dimension n ≥ 7 congruent to 3 mod 4 supports infinitely many closed simply connected manifolds of pairwise distinct homotopy type, all of which admit homogeneous metrics of Ric_k > 0 for some k < n/2. We also prove that each dimension n ≥ 4 congruent to 0 or 1 mod 4 supports closed manifolds which carry metrics of Ric_k > 0 with k ≤ n/2, but do not admit metrics of positive sectional curvature.eng© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.journal article10.1007/s00208-022-02420-w1432-1807open access